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arXiv · 1511.02084

The trace as an average over the unit sphere of a normed space with a 1-symmetric basis

Tomasz Kania·Kent E. Morrison
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Abstract

We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$ for $p\neq 2$.

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Tomasz Kania, Kent E. Morrison. 2015-11-06. The trace as an average over the unit sphere of a normed space with a 1-symmetric basis. https://doi.org/10.7153/oam-10-45

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